By: Jocelyn G

Geometry In My World…

Theorem 4-1:

If two lines intersect, then they intersect at exactly one point.

The red line and the green line intersect at the pink point. This picture is my living room window.

Theorem 5-6: Right Angles theorem

The right angle theorem states that all right angles are congruent. This means that in the picture the two blue squares representing right angles, are congruent. This makes sense, because both right angles equal 90 degrees.

This is the tile in my kitchen.

Theorem 18-1:

Triangle Angle Sum Theorem: The sum of the measures of the angles of a triangle is equal to 180 degrees.

The three green angles in the picture when added together will equal 180 degrees because it is a triangle. This picture is a present I gave to my mom in 3rd grade for Christmas.

Theorem 44-1:

This theorem states that if two polygons are similar, then the ratio of their perimeters is equal to the ratio of their corresponding sides.

The corresponding sides of these polygons are 2:1. The big tissue box has a perimeter of 72 inches so that means that the smaller tissues have a perimeter of 36 inches because if you divide 72 by 2 it is 36 and we divide it by 2 because the large tissues are twice as big as the small ones.

These tissues were in my closet to use.

Volume of a prism

2 feet

1 foot

3.5 feet

The volume of a prism is LWH. L meaning length W meaning width and H meaning height.

The volume of this suitcase is 2 feet*1 foot*3.5 feet. So the volume is calculated to be 7 cubic feet.

This is my sister’s new suitcase for her trip to Italy.

Perimeter of an irregular pentagon

As you can see from the purple lines in this picture, their are 5 sides to this shape making it a pentagon. To find the perimeter you find the length of all the sides and add them.

2 feet

6.5 inches2 feet 2 inches

6.5 inches

2 feet

6.5 inches + 2 feet + 2 feet + 6.5 inches + 2 feet 2 inches = 7 feet and 3 inches in the perimeter.

This is the counter below the house phone.

Line of Symmetry

A line of symmetry is a line that divides a plane figure into two congruent reflected halves.

The green line in this picture separated my closet door into to congruent halves, meaning that it is the line of symmetry.

Circumference of a circle

4 inches

The circumference of a circle is C=πd So the circumference of this circle is C=π(4). π can be substituted with 3.14 so the equation is C=3.14(4) which equals 12.56. The circumference of this circle is 12.56 feet.

This is a cashew box found in the cupboard.

Lateral area of a cylinder

Diameter is 3.5 inches

Height is 4 inches

The lateral area of a cylinder is L= 2πrh. In the picture it shows the diameter being 3.5 inches so to get the radius you divide by 2. The radius is 1.75 inches. The height is shown as 4 inches. Plug those into the formula and you get L= 2π(1.75)(4). Using 3.14 as pi you get L=2(3.14)(1.75)(4). Altogether this equals 43.96. So the lateral area of this cylinder is 43.96 square inches.

This is a soup can also found in my cupboard.

Surface area of a sphere

The surface area of a sphere is S=4πr2 If the radius of this basketball is 4.5 inches then we can plug it into the formula. S= 4π(4.5)2 If we also substitute 3.14 for pi then we get 4(3.14)(4.5)2

Multiplying that altogether equals 254.34 square inches for the basketball’s surface area.

I got this basketball at a Celtic’s game.

Parallel lines

Parallel lines are lines in the same plane that do not intersect.

The two purple lines in this picture are parallel.

This is my wood kitchen floor.

Nets

A net is a diagram of the faces of a three-dimensional figure arranged in such a way that the diagram can be folded to form the three-dimensional figure. This is the net of a Cheez-It box.

Center of a circle

The center of a circle is the point inside a circle that is equidistant from every point on the circle. The middle of this lamp is the bulb (circled in purple) since it is equidistant from every point on the circle it is the center of this lamp.

This lamp is in my sister’s room.

Congruent

Congruent- having the same size and shape. The two parts of the sink in the picture are both exactly the same size and shape making them congruent.

This is the kitchen sink in my house.

Convex polygon

Convex polygon- A polygon in which no diagonal contains points in the exterior of the polygon. This TV represents a convex polygon as you can see by the purple diagonals I drew in.

This is the TV in my living room.

Cube

Cube- A prism with six square faces.

This is a flower vase found in my house.

Decagon

Decagon- A ten sided polygon. A star is a great example of a decagon. This star is found hanging on the back door of my house during the holiday season!

1

23

4

5

6

78

9

10

Diameter

A segment that passes through the center of a circle and has endpoints on the circle; the length of such a segment.

The orange line of this mirror located in my living room represents the diameter of the circle

Supplementary angles

1 2

Supplementary angles are two angles whose measures have a sum of 180 degrees. In this picture I used Vienna Fingers to make supplementary angles. If you look at the picture you can see that angles 1 and 2 are supplementary because their sums add up to 180 degrees ( a straight line)

Adjacent angles

1 2

Adjacent angles are two angles in the same plane with a common vertex and a common side, but no common interior points. Angle 1 and 2 seen in the picture have these qualities therefore they are adjacent angles. This is a part of a chair in my kitchen.

For this project I got all of my pictures from items around my house. All of the information I got in the slides came from my Saxon Geometry book you provided us with in the beginning of the year.

Conclusion